I can think of a lot of good reasons for both arguments, and the Soviets made the opposite call for their lander, but what I'm interested in here is this:

Given the mass penalty of another man (body weight, supplies, oxygen, propellant) and given the LM's extreme optimization for mass, why did NASA decide that two astronauts needed to land on the moon instead of one?

Obviously this decision was made very early on in the LM's development. NASA must have known what a weight penalty this would impose, and what a crunch this would put on the rest of the vehicle. Was there just not enough confidence with the guidance systems at that time? Was there a strong sense of "you're going to need a buddy system for this to be safe"? Of course, it ended up being the right decision, as Buzz Aldrin came through during the LM's descent for Apollo 11.

$\begingroup$Several reasons, some of which you already mentioned. Annother one: redundancy. They carried spares of several mission critical components, the astronauts are no exception.$\endgroup$
– Rikki-Tikki-TaviSep 24 '15 at 14:07

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$\begingroup$The Soviets worried about their lone astronaut on the Moon. They devised a hoop that fit around the spacesuit; if the astronaut were to fall, the hoop would make sure he ended up face-down and able to get up.$\endgroup$
– HobbesSep 24 '15 at 14:35

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$\begingroup$@Hobbes That sounds like the most embarassing thing that could happen to a human: Sent to the moon only to fall down in front of a worldwide TV audience and be saved by a metal hoop.$\endgroup$
– Todd WilcoxSep 24 '15 at 17:10

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$\begingroup$The most embarrassing thing that could happen would be if the lone astronaut fell on his back and were unable to get up again because his spacesuit was too damn heavy and unwieldy.$\endgroup$
– HobbesSep 24 '15 at 17:28

3 Answers
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Dr. Robert Gilruth, Director of the Manned Spacecraft Center: "Even before the President's decision to land on the moon, we had been working on designs and guidelines for a manned circumlunar mission. This was done in a series of bull sessions on how we would design the spaceship for this purpose if the opportunity occurred. Our key people would get together evenings, weekends, or whenever we could to discuss such questions as crew size and other fundamental design factors. We believed that we would need three men on the trip to do all the work required, even before the complexity of the landing was added.

One of the reasons a crew of 3 was chosen: with 3 men, you can have a duty roster of 4 hours on, 8 hours off and have one person on duty at all times. This was seen as a requirement for longer missions. In practice, the crew preferred to synchronize their schedules, leaving the spacecraft to be monitored by ground control at times when the crew was asleep.

This book also confirms the safety aspect of having two crewmembers on the Moon.

NASA had a culture of relying heavily on crewmembers. In contrast, the Soviets tried to automate their spaceships to a greater extent (and were able to design for a smaller crew as a result).
This culture came about when the earliest group of astronauts was chosen from the test pilot community; their preference for a hands-on approach influenced the entire space program.

EVA suits are very difficult for a single person to put on by themselves, so another person was required to help the other astronaut put on their EVA suit. At the very least, it is much easier to do it with help. A single person would have a very difficult time doing this. On the ground a team of people is usually employed to have this happen. Note there are things on the back of the suit that require connections, zippers, etc. Some of these are in very difficult locations to reach.

Incidentally, this is one of the major assumptions that Andy Weir made in The Martian, that a method of putting on an EVA suit by one's self has been found by the time we try to go to Mars.

One might ask, why not wear the suit the entire time? Well, imagine being trapped inside a suit for over 24 hours (28 for Apollo 11, no doubt longer for others), and not being able to take it off at all, except for the helmet. It would get uncomfortable, influence bodily functions, etc. All in all, that is just too long to remain in a space suit if at all possible.

In addition, there are other advantages to having two people on the surface, for redundancy and to allow more to be done. The systems were only semi-automatic, which means another person was another set of eyes to make things easier. Overall, it just made sense to have two people.

$\begingroup$He also assumed that there was a way to burn Hydrazine so cleanly that you can breath the exhaust without being, dead, dead and dead. So I don't think this is a good reference.$\endgroup$
– Rikki-Tikki-TaviSep 24 '15 at 14:09

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$\begingroup$That sequence, by the way, is the one thing he most admits to getting wrong. In any case, I've posted the best sources I can find to getting as to how difficult it is.$\endgroup$
– PearsonArtPhoto♦Sep 24 '15 at 14:33

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$\begingroup$Interestingly the Soviets designed a suit that would be easier to get into unassisted: the Krechet-94.$\endgroup$
– HobbesSep 24 '15 at 14:36

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$\begingroup$Plus "what if something goes wrong?" Specifically, what if something bad "happens" to your astronaut? SciFi and movies aside, in reality there's only one practical help for that situation: another astronaut.$\endgroup$
– RBarryYoungSep 24 '15 at 23:43

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$\begingroup$This answer begs the immediate question: Why not just wear the space suit during the whole mission? Except maybe for the helmet and backpack, which I'm guessing are a lot easier to strap on. BTW your answer would benefit from a good description of a space suit. Most people seem to assume it's just a big suit, maybe kinda bulky, but in reality there are many layers to it.$\endgroup$
– DrZ214Sep 25 '15 at 3:36

I cannot comment, but I just wanted to share some information (as I just wrote a paper on Project Apollo). First, there is an excellent resource available from NASA called Chariots for Apollo. The chapter relevant to the question is Chapter 1- Concept to Challenge.

Hobbes' quote is correct, historically, that studies had been undertaken by NACA since the mid 1950s. Pearson is also partially correct that NASA wanted the workload split (for redundancy and other reasons). Project Mercury and Gemini were both adapted to the needs of Apollo. However, another great resource, though not official as per the page, is Guidelines for Advanced Manned Space Vehicle Program. You will want to pay special attention paper written by Stanley C. White Human-Factors Considerations.

NASA decided on two astronauts for many reasons, with only some given by Hobbes and Pearson. Hopefully, the provided resources will help explain some other reasons aside from the work and abilities of the astronauts.

Personally, and without justification, I feel NASA chose multiple astronauts because they did not understand how extended and stressful missions in space might affect a human. I believe this is somewhat shown by the following example. NASA quarantined all Apollo astronauts for 21 days, up until they realized there was no chance for them to bring back anything dangerous.

I also feel their answers ignore the political ramifications behind Apollo (NASA was pressured to meet the decade goal), but that is a topic for another day.

In response to the mass penalty, from the provided resources you can see that NACA and subsequently NASA originally prepared for a mission with far more available resources. Mass in the preparatory stages was not considered to be an issue. The Goett Committee fully expected a two week long mission (against the 8 day Apollo 11 mission).